What are the Multiples of 17?
When the number 17 is multiplied by any natural number, the result is known as a multiple of 17. A multiple of 17 can be written as 17n where n can be any natural number. If we write first n multiples of 17 that indicates we have to multiply 17 with the first n natural numbers.
For example:
If we multiply 17 by 6, then the product is 102. As a result, we define 102 as a multiple of 17. Another thing to remember here is that the product of two numbers is a multiple of both numbers. Hence, 102 is a multiple of 17 as well.
The multiples of 17 can be expressed in the form of 17n, where n is a natural number.
And if, n = 1, 2, 3, 4, 5, 6, …
then the multiples of 17 will be:
17, 34, 51, 68, 85, 102, 119, 136, …
Thus, from the above observations, we can say that the multiple of 17 can be obtained by multiplying natural numbers with 17.
Also, we can observe that the difference between each succeeding number and the preceding number is 17, that is,
34 – 17 = 17,
51 – 34 = 17,
68 – 51 = 17, and so on.
For example 119, 136, and 153 are all multiples of 17 because we can get these numbers mentioned here by multiplying 17 with specific natural numbers.
17 x 7 = 119 | 17 multiplied by 7 to get 119 |
17 x 8 = 136 | 17 multiplied by 8 to get 136 |
17 x 9 = 153 | 17 multiplied by 9 to get 153 |
Finding Multiples of 17 by Repeated Addition
Repeated addition means adding a number to itself, in a repetitive manner. So we can also use repeated addition to find the multiple of a number.
If we want to find the first ten multiples of 17, we can write it in following way:
17 x 1 | 17 | |
17 x 2 | 17 + 17 | Here 17 added two times |
17 x 3 | 17 + 17 + 17 | Here 17 added three times |
17 x 4 | 17 + 17 + 17 + 17 | Here 17 added four times |
17 x 5 | 17 + 17 + 17 + 17 + 17 | Here 17 added five times |
17 x 6 | 17 + 17 + 17 + 17 + 17 + 17 | Here 17 added six times |
17 x 7 | 17 + 17 + 17 + 17 + 17 + 17 + 17 | Here 17 added seven times |
17 x 8 | 17 + 17 + 17 + 17 + 17 + 17 + 17 + 17 | Here 17 added eight times |
17 x 9 | 17 + 17 + 17 + 17 + 17 + 17 + 17 + 17 + 17 | Here 17 added nine times |
17 x 10 | 17 + 17 + 17 + 17 + 17 + 17 + 17 + 17 + 17 + 17 | Here 17 added ten times |
The n\(^{\text{th}}\) multiple of 17
The n\(^{\text{th}}\) multiple of 17 can be obtained by either multiplying 17 by n or by adding 17 n times;
n\(^{\text{th}}\) multiple of 17 = 17 x n, or
n\(^{\text{th}}\) multiple of 17 = 17 + 17 + ……… n times
[Note: n is any natural number.]
List of the First 10 Multiples of 17
17 x 1 | 17 |
17 x 2 | 34 |
17 x 3 | 51 |
17 x 4 | 68 |
17 x 5 | 85 |
17 x 6 | 102 |
17 x 7 | 119 |
17 x 8 | 136 |
17 x 9 | 153 |
17 x 10 | 170 |
Solved Multiples of 17 Examples
Example 1: Is 55 a multiple of 17?
Solution:
List multiples of 17.
17, 34, 51, 68, 85, 102, …
So, 55 is not a multiple of 17.
Example 2: What is the 8th multiple of 17?
Solution:
The 8th multiple of 17 can be obtained by the repeated addition of 17 for 8 times;
17 + 17 + 17 + 17 + 17 + 17 + 17 + 17 = 136
Hence, the 8th multiple of 17 is 136.
Example 3: John, Tom, Ray, and Annie, four friends, decided to buy chocolates in the order of the first four multiples of 17. Can you make a list of how many chocolates each of them bought?
Solution:
The first four multiples of 17 are 17, 34, 51, and 68.
So, John bought 17 chocolates.
Tom bought 34 chocolates.
Ray bought 51 chocolates.
Annie bought 68 chocolates.
The multiples of a number are obtained by multiplying the number with a natural number.
If a number is multiplied with another number then the resultant product is known as a multiple and those multiplied numbers are known as factors of the resultant product.
For example, 17 x 3 = 51
51 is a multiple of both 3 and 17.
3 and 17 are factors of 51.
The smallest multiple of 17 is 17 itself.
A number can be multiplied indefinitely so it can have an infinite number of multiples.